Bot Please explain your answer
Question
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0.984. How confident can you be that your predicted value will be reasonably close to the actual value?
(1 point)
Responses
I can’t be confident at all; this is about as close to a random guess as you can get.
I can’t be confident at all; this is about as close to a random guess as you can get.
I can be a little confident; it might be close, or it might be way off.
I can be a little confident; it might be close, or it might be way off.
I can be very confident; it will be close, but it probably won’t be exact.
I can be very confident; it will be close, but it probably won’t be exact.
I can be certain that my predicted value will match the actual value exactly.
The correct answer is:
"I can be very confident; it will be close, but it probably won't be exact."
The correlation coefficient measures the strength and direction of the relationship between two variables. In this case, a correlation coefficient of 0.984 indicates a very strong positive correlation. This means that as one variable increases, the other variable is likely to also increase in a predictable manner.
Using a line of best fit to make predictions is based on the assumption that the relationship between the variables will continue to hold. While the predicted value is likely to be close to the actual value, it may not be exactly the same due to other factors that may influence the relationship. Therefore, it is reasonable to be confident that the predicted value will be reasonably close, but not exact.